\(\Leftrightarrow sin\left(2x-\frac{\pi}{4}\right)=\frac{2}{5}\)
\(\Rightarrow\left[{}\begin{matrix}2x-\frac{\pi}{4}=arcsin\left(\frac{2}{5}\right)+k2\pi\\2x-\frac{\pi}{4}=\pi-arcsin\left(\frac{2}{5}\right)+k2\pi\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=\frac{\pi}{8}+\frac{1}{2}arcsin\left(\frac{2}{5}\right)+k\pi\\x=\frac{5\pi}{8}-\frac{1}{2}arcsin\left(\frac{2}{5}\right)+k\pi\end{matrix}\right.\)